Ultrasound calibration and real-time quality assurance based on closed form formulation

ABSTRACT

Disclosed is a system and method for intra-operatively spatially calibrating an ultrasound probe. The method includes determining the relative changes in ultrasound images of a phantom, or high-contrast feature points within a target volume, for three different ultrasound positions. Spatially calibrating the ultrasound probe includes measuring the change in position and orientation of the probe and computing a calibration matrix based on the measured changes in probe position and orientation and the estimated changes in position and orientation of the phantom.

This application claims the benefit to International Patent ApplicationNo. PCT/US2005/013026, filed on Apr. 15, 2005 and U.S. ProvisionalPatent Application No. 60/562,460, filed on Apr. 15, 2004, both of whichare hereby incorporated by reference for all purposes as if fully setforth herein.

The research and development effort associated with the subject matterof this patent application was supported by the National ScienceFoundation under grant no. ERC 9731478.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention involves the field of ultrasound imagery. Moreparticularly, the present invention involves spatial calibration ofultrasound probes for intra-operative use.

2. Discussion of the Related Art

Computer Integrated Surgery has revolutionized surgical procedures,whereby 3D imagery of a target volume is created to enable a surgeon tomore precisely and accurately position surgical tools within a patient.To serve this purpose, the imaging system, or guidance modality, shouldprovide 3D imagery in real time; it must not be excessively obstructiveor burdensome in an operating environment; and it must provide 3Dimagery with sufficient accuracy and precision to provide effectivesurgical planning and execution.

Ultrasound has become a popular guidance modality for medicalprocedures, due to its real-time operation, safety, low cost, andconvenience of use in an operating room environment. Although it is nota “true 3D” imaging modality, such as Magnetic Resonance Imaging (MRI)and Computer Tomography (CT), techniques have been developed to convertmultiple ultrasound 2D images into a 3D image in order to provide imageguidance for surgeons while exploiting the benefits and conveniences ofultrasound.

Components of a conventional ultrasound system 100 are illustrated inFIG. 1. The ultrasound system 100 includes a transmitter 105 having atransmitter reference frame 130; and an ultrasound probe 110 having aprobe reference frame 135. The ultrasound probe 110 transmits andreceives energy in a scan plane 142, and projects a plurality of pixels140 in a pixel reference frame 145. A conventional ultrasound system 100may also include tracking sensors 125 to monitor the position andorientation of the ultrasound probe 110. The ultrasound system 100 isused to collect multiple 2D ultrasound images, which are assembled intoa 3D image space 155 having a construction reference frame 150(hereinafter “construction frame”).

In order to provide image guidance during a surgical procedure, 2Dultrasound images acquired by the ultrasound system 100 must beregistered or mapped in real-time into a 3D image space 155, whichencompasses a target volume within the patient undergoing surgery.Although there are ultrasound probes that acquire 3D images, theseprobes need to be spatially calibrated as well. Registering pixels frompixel reference frame 145 to the 3D image space 155 requires atransformation matrix encompassing a series of constituent coordinatetransformation matrices: e.g., from the pixel frame 145 to theultrasound probe reference frame 135; from the ultrasound probe frame135 to the transmitter reference frame 130; and from the transmitterreference frame 130 to the construction frame 150. Of thesetransformation matrices, the most difficult to determine is thetransformation matrix from the pixel reference frame 145 to theultrasound probe reference frame 135 (hereinafter the “probe calibrationmatrix”).

According to the related art, spatial calibration is the act ofdetermining each of the aforementioned transformation matrices, which istypically done before a medical procedure. In related art spatialcalibration, the ultrasound probe 110 is placed and oriented such thatit acquires an image of a calibration target, or phantom, which has welldefined spatial features. Using image processing techniques such assegmentation, the well defined features of the phantom are identifiedand located in the acquired ultrasound image, and the position andorientation of the phantom is derived from the segmented image. In therelated art approach, images are acquired with the ultrasound probe 110placed in a single position and orientation. If the position andlocation of the phantom are known relative to the construction frame155, the probe calibration matrix can be derived. By comparing thelocations of the identified imaged features of the phantom with knownlocations and relative orientations of these features, the orientationof the phantom may be determined relative to the orientation of theultrasound probe, and the probe calibration matrix may be derived bycorrelating the segmented images of the phantom with the phantom's knownspatial characteristics.

Image processing techniques such as segmentation are computationallyintensive and may not be feasible to compute in real time, based on thenumber of images acquired. Typical segmentation is performed on severalhundred images. The large number of images not only requires time toprocess, but it increases the likelihood of errors that may render theprobe calibration matrix invalid.

According to the related art, once the transformation matrices,including the probe calibration matrix, are known, a pixel 140 may beregistered into the 3D image space 155 defines by the construction frame150. The transformation of a pixel 140 location from the pixel referenceframe 145 to the construction frame 155 can be expressed as:C_(x)=^(C)T_(T) ^(T)T_(R) ^(R)T_(P)P_(x),where P_(x) is the location of pixel 140 in pixel reference frame 145;C_(x) is the location of pixel 140 in construction frame 155; ^(R)T_(P)is the coordinate transformation matrix from the pixel reference frame145 to the ultrasound probe reference frame 135 (i.e., the probecalibration matrix); ^(T)T_(R) is the coordinate transformation from theultrasound probe reference frame 135 to the transmitter reference frame130, which may be measured using tracking sensors 125; and ^(C)T_(T) isthe coordinate transformation from the transmitter reference frame 130to the construction frame 155, which may be measured.

The accuracy and precision of registering ultrasound image pixels 140into the construction frame 155 is limited by the accuracy and precisionof each of the above transformation matrices. The weakest link in thischain is the accuracy and precision of the probe calibration matrix^(R)T_(P). Accordingly, a primary challenge in spatial calibration is indetermining the probe calibration matrix ^(R)T_(P).

There are errors intrinsic to the conventional spatial calibrationprocess that limit its precision and accuracy, including the following:imprecision in fabrication of the phantom, subsequent mechanicaldistortions of the phantom, lack of precision in characterizing thefeatures of the phantom, spatial co-registration or ambiguities, andlimits to numerical solution optimizations. As such, the quality of thecalibration is limited to the accuracy and precision to which thephantom is characterized.

An additional disadvantage of the related art spatial calibration isthat since it cannot be performed intra-operatively, partly because itcannot be performed in real time, it is vulnerable to subsequent changesthat may render any or all of the calibration matrices invalid withoutwarning. Such post-calibration changes may be brought on by mechanicalalteration to the tracking sensors and changes in tissue temperature.The effect of post-calibration changes may include inaccurate 3D image,resulting in incorrect surgical instrument placement.

Although the above discussion involves ultrasound, the same issues maybe encountered for any imaging system for which 2D images are assembledinto a 3D image space. Or more generally, the same issues may arise inwhich a 2D imaging system is spatially calibrated in order to registerimage products into another reference frame.

SUMMARY OF THE INVENTION

Accordingly, the present invention is directed to ultrasound calibrationand real-time quality assurance based on closed form formulation thatsubstantially obviates one or more of the problems due to limitationsand disadvantages of the related art. In general, the present inventionachieves this by deriving a probe calibration matrix ^(R)T_(P) based onrelative images of a phantom acquired from at least three positions andorientations, as opposed to deriving a probe calibration matrix^(R)T_(P) from images of the phantom, from one position and orientation,that is correlated with known characteristics of the phantom.

An advantage of the present invention is to provide more reliablereal-time ultrasound-based 3D imagery for use during medical proceduresin that the ultrasound probe may be spatially calibratedintra-operatively. This helps mitigate post-calibration changes that maydegrade the accuracy of 3D imagery without warning.

Another advantage of the present invention is to provide a moreefficient and robust spatial calibration of an ultrasound probe. Byspatially calibrating the ultrasound probe based on the relativedifferences between two or more images of the same phantom, theresulting calibration is less dependent on the precision to which thespatial characteristics of the phantom are known.

Another advantage of the present invention is to simplify the ultrasoundprobe calibration process. The present invention identifies pixelscorresponding to prominent feature points on a phantom, as opposed tosegmenting an image in order to reconstruct an image of the phantom,which is more computationally intensive.

Additional features and advantages of the invention will be set forth inthe description which follows, and in part will be apparent from thedescription, or may be learned by practice of the invention. Theobjectives and other advantages of the invention will be realized andattained by the structure particularly pointed out in the writtendescription and claims hereof as well as the appended drawings.

To achieve these and other advantages and in accordance with the purposeof the present invention, a method for spatially calibrating anultrasound probe comprises placing the ultrasound probe in a firstposition and orientation relative to a phantom; measuring the firstposition and orientation of the ultrasound probe; acquiring a firstultrasound image of the phantom; determining a first transformationmatrix corresponding to a phantom reference frame and a pixel referenceframe, based on the first ultrasound image; repositioning the ultrasoundprobe in a second position and orientation relative to the phantom;measuring the second position and orientation of the ultrasound probe;acquiring a second ultrasound image of the phantom; determining a secondtransformation matrix corresponding to the phantom reference frame andthe pixel reference frame, based on the second ultrasound image; andcomputing a probe calibration matrix based on the first position andorientation of the ultrasound probe, the first transformation matrix,the second position and orientation of the ultrasound probe, and thesecond transformation matrix.

In another aspect of the present invention, a system for performingintra-operative calibration of an ultrasound probe comprises a positionand angle encoder for measuring a position and angle of the ultrasoundprobe; and a data system having a computer readable medium encoded witha program for computing a probe calibration matrix according to a closedform formulation, and according to relative changes between thelocations of prominent feature points in a first and a second ultrasoundimage, wherein the first ultrasound image corresponds to a firstultrasound probe position, and the second ultrasound image correspondsto a second ultrasound probe position.

It is to be understood that both the foregoing general description andthe following detailed description are exemplary and explanatory and areintended to provide further explanation of the invention as claimed.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are included to provide a furtherunderstanding of the invention and are incorporated in and constitute apart of this specification, illustrate embodiments of the invention andtogether with the description serve to explain the principles of theinvention.

FIG. 1 illustrates components of an ultrasound imaging system accordingto the related art;

FIG. 2 illustrates an exemplary ultrasound imaging system according tothe present invention;

FIG. 3 illustrates an exemplary spatial calibration process according tothe present invention;

FIG. 4 illustrates an exemplary phantom according to the presentinvention;

FIG. 5 illustrates an exemplary ultrasound imaging system, whichincludes at least one docking station;

FIG. 6 illustrates an exemplary ultrasound imaging system that usesdouble-wedge phantoms;

FIGS. 7A-7D illustrate the effects of misalignment and offset between anultrasound probe and a double-wedge phantom, and their effects;

FIGS. 8A-D illustrate ultrasound images, and how misalignment and offsetbetween an ultrasound probe and a double-wedge phantom are apparent inthe images;

FIG. 9 illustrates an exemplary double-wedge phantom according to thepresent invention; and

FIG. 10 illustrates an exemplary process for performing bootstrapcalibration of an ultrasound probe according to the present invention.

DETAILED DESCRIPTION OF THE ILLUSTRATED EMBODIMENTS

FIG. 2 illustrates an exemplary ultrasound imaging system 200 accordingto the present invention. The imaging system 200 includes an ultrasoundtransmitter 205 having a transmitter reference frame 230; an ultrasoundprobe 210 having a probe reference frame 235; position and angleencoders 216 for measuring the position and orientation of the probereference frame 235 relative to the transmitter reference frame 230; anultrasound processor 215 for providing power and signals to, andreceiving signals from, the ultrasound transmitter 205 and theultrasound probe 210; a data system 220 for sending commands to andreceiving data from the ultrasound processor 215 and the position andangle encoders 216; and a user interface 225 connected to the datasystem 220. The ultrasound probe 210 may transmit and receive energy ina scan plane 242, which includes a plurality of pixels 240 within thescan plane 242 and having a pixel reference frame 245.

The exemplary system 200 acquires ultrasound images, through use of theultrasound probe 210, within a 3D image space 255 having a constructionreference frame 250. Further, the exemplary system 200 may include oneor more phantoms 260 and 265, which are located such that they can beimaged by the ultrasound probe 210, and wherein the phantoms 260 and 265may be acoustically coupled to a target (not shown) to be imaged withinthe 3D image space 255. By acoustically coupling, it is understood thatcontinuity in the propagation medium is maintained such that sound wavespass through.

FIG. 2 further illustrates a single ultrasound probe 210 in two separatepositions, Position 1 and 2, in which the probe 210 may acquire imagesof the phantoms 260 and 265. Instead of two phantoms, there may be asingle phantom, which may be imaged by the ultrasound probe 210 frommultiple positions and orientations. For purposes herein, phantom 260will be referred to in the case in which there is a single phantom.Although two positions are illustrated, at least three positions aregenerally required for computing the probe calibration matrix ^(R)T_(P)according to the present invention.

As used herein, the term “matrix,” as in the probe calibration matrix^(R)T_(P), may refer to any representation of a spatial relationshipbetween coordinate frames, such as a quaternion.

For the purposes of illustration, this embodiment of the presentinvention may employ a SONOLINE™ Antares ultrasound scanner manufacturedby Siemens Medical Solutions, USA, Inc., Ultrasound Division, Issaqua,Wash. with a Siemens VF 10-5 linear array probe held in a rigidattachment mounted on an adjustable arm. However, it will be readilyapparent to one skilled in the art that other commercially availableultrasound scanners may be used.

In this exemplary embodiment of the present invention, the position andangle encoders 216 include multiple optical markers attached to theultrasound probe 210, which are tracked using, for example, an OPTOTRAK™device, manufactured by Northern Digital, Inc. It will be readilyapparent to one skilled in the art that alternate devices and systemsfor providing real-time measurements of position and orientation of theultrasound probe 210 may be used and are within the scope of the presentinvention.

The data system 220 may include one or more computers, which may benetworked together either locally or over a network. The data system 220includes software (hereinafter “the software”) for implementingprocesses according to the present invention. The software may be storedand run on the data system 220, or may be stored and run in adistributed manner between the data system 220, the ultrasound processor215, and the user interface 225.

FIG. 3 illustrates an exemplary process 300 for providing real-timespatial calibration according to the present invention, which may beimplemented by the software. Process 300 may be used in conjunction withsystem 200, illustrated in FIG. 2, in which a single phantom 260 isused.

In step 310, the ultrasound probe 210 is placed in position 1 of N,wherein N may be at least three. Position 1 may be arbitrary orpredetermined. Either way, the position should be such that the phantom260 is within the scan plane 242 of ultrasound probe 240 whereinprominent feature points within the phantom 260 are readily identifiablein the acquired ultrasound image.

In step 320, the software acquires position and angle data of ultrasoundprobe 210 from the position and angle encoders 216 and stores thecorresponding data values in memory. The software may acquire and storeposition and angle data of the ultrasound probe 210 exclusively whilethe ultrasound probe 210 is in position 1, or the software maycontinuously acquire and store position and angle data values throughoutexemplary process 300. The software may provide time tag informationcorresponding to the position and angle data such that the time tag datamay be used to synchronize the position and angle data with theultrasound data acquired from the ultrasound processor 215.

In step 330, the ultrasound processor 215 acquires and processesultrasound image data from the ultrasound probe 210 while the ultrasoundprobe is held in position 1. The software then receives ultrasound imagedata from the ultrasound processor 215 and stores the corresponding datavalues in memory. The software may acquire ultrasound data continuouslythroughout exemplary process 300, along with time tag data, and maystore the ultrasound and time tag data values so that the ultrasounddata may be synchronized with similarly time tagged position and angledata acquired from the position and angle encoders 216. If the datasystem 220 continuously acquires and stores ultrasound data valuesthroughout exemplary process 300, the data system may additionallyacquire and store data from the user interface 225, along withcorresponding time tag data, which may provide a flag indicating thatultrasound data values corresponding to a given time were acquired whilethe ultrasound probe was in position 1.

In step 340, prominent feature points corresponding to the phantom 260are identified from the ultrasound data acquired in step 330, asillustrated in FIG. 4. The prominent feature points may be selected bythe user via the user interface 225 by, for example, selecting the pointwith a cursor and mouse-click. Alternatively, the software mayautomatically identify prominent feature points using image processingtechniques that are known to the art.

FIG. 4 illustrates an exemplary phantom 260, along with its referenceframe 410, and a scan plane 242 impinging on the phantom 260. In aparticular embodiment, the phantom 260 may include a matrix of N-shapedwires stretched between two parallel plates. In order for the phantom260 to be used intra-operatively, it should be acoustically coupled witha target volume, such as a patient undergoing surgery, such that theuser may periodically position the ultrasound probe 210 in a givenposition 1 and position 2 during an operation. When being imaged by theultrasound probe 210, the scan plane 242 may intersect a plane definedby the phantom at points E, K, and Z, as illustrated in FIG. 4. The xand y coordinate of the center point K of the phantom 260 in the phantomreference frame 410 may be determined from the relations:x _(k) =x _(b)+(KE/EZ)·(x _(c) −x _(b)), and y _(k) =y _(b)+(KE/EZ)·(y_(c) −y _(b)),in which x_(k) and y_(k) are the coordinates of the center image point Kof the phantom 260 in the phantom reference frame 410; x_(b) and y_(b)are the coordinates of point B on the phantom 260 in the phantomreference frame 410; and x_(c) and y_(c) are the coordinates of point Con the phantom 260 in the phantom reference frame 410.

In step 350, with the coordinates of the center point K determined, thesoftware then computes a coordinate transformation between theultrasound probe reference frame 245 and the phantom reference frame410. The transformation may be accomplished by, for example, Horn'squaternion rigid registration method, as described in B. Horn,Closed-form solution of absolute orientation using unit quaternions,Journal of the Optical Society of America A, Vol. 4, page 629, April1987, which is incorporated herein by reference. Other techniques may beused, such as those employed to transform a set of points betweencoordinate systems, as is done in the fields of photogrammetry. Theresult of this transformation is a translation and rotation of the imageof the phantom 260 from the phantom reference frame 410 to the pixelreference frame 245.

In step 360, the software determines if there are more positions atwhich to acquire ultrasound data. If so, steps 310-350 are repeated fora new position. The next position may be chosen arbitrarily, ordetermined prior to executing the exemplary process 300. The nextposition should be chosen such that the phantom 260 is located withinthe scan plane 242 of the ultrasound probe 210, and that prominentfeature points on the phantom 260 will be visible in the ultrasoundimagery acquired by the ultrasound probe 210, as illustrated in FIG. 4.In a particular embodiment of the present invention, steps 310-350 areiterated 3 times.

In step 375, the software retrieves the stored data values for thefollowing: the translation and rotation of the phantom 260 from thephantom reference frame 410 to the pixel reference frame 245 when theultrasound probe 240 was in each position; and the position and angle ofthe ultrasound probe 240, as measured by the position and angle encoders216, when the ultrasound probe was in each position

In step 375, the software assembles this data into a closed formformulation for determining the probe calibration matrix ^(R)T_(P)according to the present invention and then derives the probecalibration matrix ^(R)T_(P) from the closed form formulation. Theclosed form formulation is based on the homogeneous matrix equationAX=XB, in which A is the relative coordinate transformations between thelocations of the respective pixels corresponding to the prominentfeature points of the phantom; B is the relative coordinatetransformation between ultrasound prove reference frame at position 1and position 2, as measured by the position and angle encoders; and X isthe probe calibration matrix ^(R)T_(P). This homogeneous matrix equationmay be expressed in software as the following:

${\begin{bmatrix}{I_{9} - {R_{a\; 12} \otimes R_{b\; 12}}} & 0_{9 \cdot 3} & 0_{9 \cdot 3} \\{I_{3} \otimes t_{b\; 12}^{t}} & {I_{3} - R_{a\; 12}} & {- D_{u\; 12}} \\{I_{9} - {R_{a\; 23} \otimes R_{b\; 23}}} & 0_{9 \cdot 3} & 0_{9 \cdot 3} \\{I_{3} \otimes t_{b\; 23}^{t}} & {I_{3} - R_{a\; 23}} & {- D_{u\; 23}}\end{bmatrix}\begin{pmatrix}{{vec}\left( R_{x} \right)} \\t_{x} \\\lambda\end{pmatrix}} = \begin{pmatrix}0_{9 \cdot 1} \\0_{3 \cdot 1} \\0_{9 \cdot 1} \\0_{3 \cdot 1}\end{pmatrix}$where I is an identity matrix; R_(a12) and R_(a23) are the rotations ofthe pixel reference frame 245 from position 1 to position 2, and fromposition 2 to position 3, respectively; R_(b12) and R₂₃₂ are therespective rotations of the probe reference frame 235 from position 1 toposition 2 and from position 2 to position 3, as measured by theposition and angle encoders 216; t_(b12) ^(t) and t_(b23) ^(t) arerespectively the transverse of the translation vectors corresponding tothe translation of the probe reference frame 235 from position 1 toposition 2 and from position 2 to position 3, as measured (for example,in mm) by the position and angle encoders 216; D_(u12) and D_(u12) arethe translation vectors of the pixel reference frame 245 going fromposition 1 to position 2; t_(x) is the translation vector componentcorresponding to the calibration matrix (to be solved); R_(x) is therotational component corresponding to the calibration matrix (to besolved); and λ is a vector of translational scale factors, wherein eachscale factor converts the translation from number of pixels to adistance, such as millimeters. Of these variables, R_(a) and D_(u) areobtained by estimating the translation and rotation of the prominentfeature points of the phantom 260 between position 1 and 2; and R_(x),t_(x), and λ are the values to be solved using the above formulation.The

symbol refers to the Kronecker product of two matrices; and the vec( )operator creates a column vector from a matrix as follows:

${{vec}(A)} = \begin{bmatrix}a_{11} \\a_{12} \\\vdots \\a_{1\; m} \\a_{21} \\a_{22} \\\vdots \\a_{n\; m}\end{bmatrix}$

The rotation and translation corresponding to the probe calibrationmatrix ^(R)T_(P) may be derived by extracting a unique solution from thenull space associated with the above formulation using the unityconstraint to the first nine coefficients representing the rotationR_(x). As is known in the art, extracting the null space involvessolving the closed form solution and selecting the vector correspondingto the lowest coefficient.

If more than three positions are to be used, the left-most array in theclosed form solution may be concatenated to include the I₉−R_(a12)

R_(b12) 0_(9·3) 0_(9·3) and I₃

t_(b12) ^(t) I₃−R_(a12)−D_(u12) expressions for subsequent motions toadditional positions. Generally, the more motions used, the more precisethe probe calibration matrix ^(R)T_(P), at the expense of speed ofcomputation.

An alternate approach is to solve the above formulation in two steps,wherein the rotation R_(x) is extracted first, and then the translationt_(x) and its associated scale factor λ are subsequently extracted. Bysolving for and extracting the scale factor vector λ, the calibrationmatrix may account for non-rigidity of the transformation between thepixel reference frame 245 and the probe reference frame 235, as opposedto a rigid transformation, in which case the scale factor λ may be ascalar. The rigid transformation case is described in the context ofrobotic hand-eye coordination by N. Andreff, R. Horaud, and B. Espiau,Robotic Hand-Eye Calibration Using Structure-from-Motion, TheInternational Journal of Robotics Research, Vol. 20, No. 3, pp. 228-248,the contents of which are incorporated herein by reference.

With the rotation R_(x), t_(x) translation, and scale factor vector λderived from the null space of the above formulation, the probecalibration matrix ^(R)T_(P) may be assembled according to the followingrelation:

${{}_{}^{}{}_{}^{}} = {\begin{bmatrix}\; & \; & \; & t_{x} \\\; & R_{x} & \; & t_{y} \\\; & \; & \; & t_{z} \\0 & 0 & 0 & 1\end{bmatrix} = \begin{bmatrix}\; & \; & \; & {\lambda_{x}u_{x}} \\\; & R_{x} & \; & {\lambda_{y}u_{y}} \\\; & \; & \; & {\lambda_{z}u_{z}} \\0 & 0 & 0 & 1\end{bmatrix}}$where (ux, uy, uz) is the translation vector in number of pixels, andthe scale factor λ converts the number of pixels into distance, such asmillimeters.

The software may then store the constituent values of the probecalibration matrix ^(R)T_(P) for use in subsequent pixel registrationfrom the pixel reference frame 245 into the 3D image space 255 definedby the reference frame.

FIG. 5 illustrates still another embodiment of the present invention,where exemplary system 200 includes one or more docking stations 510 and520. The docking stations 510 and 520 are each in a substantially fixedposition and orientation relative to the phantom 260, and each includesan acoustically coupled fixture for placing the ultrasound probe 210 ina precise position and angle relative to the construction frame 255. Forexample, by having two docking stations 510 and 520, one at position 1and another at position 2, the user may place the ultrasound probe 210more precisely at each of the two positions, which may improve theprecision and accuracy of the measured position and orientation of theprobe reference frame 245.

Multiple ultrasound images may be acquired per position, with each imagebeing used to compute a separate probe calibration matrix. For example,if 3 positions are used, and 10 images are acquired per position, thenit is possible to compute 10×9×8=720 probe calibration matrices.Similarly, if 6 images are taken per position, if 3 positions are used,then 6×5×4=120 probe calibration matrices may be generated. Computingthe mean and standard deviation of any or all of these probe calibrationmatrices will provide an indication of the precision of the calibration.

FIG. 6 illustrates another embodiment of the present invention, in whichimaging system 600 includes certain substantially similar components toexemplary system 200. However, system 600 also includes threedouble-wedge phantoms 610 mounted on a base plate 620, which has a baseplate reference frame 630; and a cross-wire structure 640, which islocated such that it may be imaged by the ultrasound probe 210simultaneously with any of the double-wedge phantoms 610. The base plate620 may have holes located and so that double-wedge phantoms 610 may beaffixed to the base plate 620. The double-wedge phantoms 610 may beprecisely located so that their relative locations are precisely known.In a particular embodiment, the double-wedge phantoms 610 are rigidlymounted so that their relative locations are known to within 100 μm. Thedouble-wedge phantoms 610 and the base plate 620 may be immersed in anacoustically coupling material, such as a gel or water.

Exemplary system 600 may be used in conjunction with exemplary process300. In using exemplary system 600, the ultrasound probe 210 ispositioned and oriented to acquire images of the double wedge phantom610 at pose 1 in step 310. As used herein, “pose” refers to the positionand orientation of a given double-wedge phantom 610. Ultrasound imagesand probe position and angle data is then acquired in steps 320-350.Steps 310-350 may be iterated, whereby the position and orientation ofthe ultrasound probe 210 may be adjusted based on the translation androtation determined in step 350.

In step 340, the images of the double-wedge phantom 610 are identifiedin an ultrasound image. FIGS. 7A-7D illustrate different scenarios inwhich an ultrasound beam 705 transmitted by the ultrasound probe 210impinges on wedge features 710 and 720 of double-wedge phantom 610, andhow the reflected energy from the transmitted beam 705 is distributed.FIGS. 8A-8D illustrate how the wedges 710 and 720 may appear in aresulting ultrasound image 732.

Given the shape of the double-wedge phantom 610, any translationaloffset or angular misalignment in the transmitted beam 705 relative tothe pose of the double-wedge phantom 610 is manifested in the ultrasoundimage 732. By using the ultrasound image 732 as a form of feedback, theposition and orientation of the probe 210 may be adjusted to correct itfor any misalignment and translational offset.

FIGS. 7A and 8A correspond to a scenario in which the transmitted beam705 is aligned with the pose of the double-wedge phantom 610 with notranslational offset. Line 721 refers to the “early echo,” or the firstreflected energy of the transmitted beam 705 to impinge on either wedge710 and 720. Line 722 refers to the “late echo,” or the end of thereflected energy from the transmitted beam 705. Elements 725 a and 725 brefer to the geometry of the reflected energy, in which the dimension Lcorresponds to the length of the reflected energy, which is a functionof the beam width BW and the slope of the wedge 710 or 720.

FIG. 8A illustrates an exemplary ultrasound image 732 corresponding toFIG. 7A. In FIG. 8A, the acoustic energy reflected from wedge 710results in a “cloud” image 730 a; and the acoustic energy reflected fromwedge 720 results in cloud 730 b. Features 730 a and 730 b are referredto as clouds since the acoustic energy in transmitted beam 705 spatiallyand temporally spreads as a result of the divergence of the transmittedbeam 705, the shape of the acoustic pulse transmitted by the ultrasoundprobe 210, and the angle of the wedge from which the energy isreflected. Since the transmitted beam 705 is aligned with the pose ofthe double-wedge phantom, clouds 730 a and 730 b have substantially thesame height, which corresponds to dimension L, which is due to the factthat the transmitted beam 705 impinges on wedges 710 and 720 atsubstantially the same (and opposite) angle. Further, clouds 730 a and730 b are located substantially “side by side” in ultrasound image 732,which is due to the fact that there is substantially no translationaloffset between the center of the transmitted beam 705 and the point atwhich wedges 710 and 720 cross.

The beam width BW of the transmitted beam may be computed from theheight L of clouds 730 a and 730 b according to the relationBW=L·tan(30°). It will be readily apparent that angles other than 30°may be used, which may result in differing sensitivities to angularmisalignment and translational offset.

FIG. 7B illustrates how acoustic energy may be reflected from wedges 710and 720 when the transmitted beam 705 is angularly aligned with the poseof the double-wedge phantom 610, but in which the transmitted beam 705has a translational offset relative to wedges 710 and 720. In FIG. 8B,clouds 730 a and 730 b have substantially the same height, but areoffset from one another in a manner proportional to the translationaloffset of the transmitted beam 705.

FIG. 7C illustrates how acoustic energy may be reflected from wedges 710and 720 when the transmitted beam is angularly misaligned (at angle α)with the pose of the double-wedge phantom 610, but does not have anytranslational offset. As illustrated in FIG. 8C, clouds 730 a and 730 bhave different heights S and B, wherein the height differential isproportional to the misalignment angle according to the followingrelation:

$\frac{\tan\left( {{30{^\circ}} - \alpha} \right)}{\tan\left( {{30{^\circ}} + \alpha} \right)} = \frac{S}{B}$where 30° is the magnitude of the angle of wedges 710 and 720. Asmentioned earlier, angles other than 30° may be used, which may resultin different sensitivities to angular misalignment and translationaloffset.

FIG. 7D illustrates how acoustic energy may be reflected from wedges 710and 720 with a transmitted beam 705 impinging on the double-wedgephantom 610 with both an angular misalignment with the pose of thedouble-wedge phantom 610 and an translational offset. As illustrated inFIG. 8D, the resulting clouds 730 a and 730 b in the ultrasound image732 have different heights S and B, the difference of which isproportional to the misalignment angle; and the clouds 730 a and 730 bare offset in a manner proportional to the translational offset of thetransmitted beam 705.

In step 350, the heights of the clouds 730 a and 730 b, and theiroffset, may be determined automatically through image processingtechniques known to the art. Alternatively, the heights of the clouds730 a and 730 b and their offset may be determined by having the userplace a cursor on the top and bottom of clouds 730 a and 730 b, andclick a mouse. With the cloud size differential and cloud offsetdetermined, the translation and rotation from the reference frame of thedouble-wedge phantom 610 to the pixel reference frame 245 may bedetermined.

According to this exemplary embodiment of the present invention, theuser may adjust the position and orientation of the ultrasound probe 210to substantially eliminate the angular misalignment and translationaloffset of the ultrasound probe 210 relative to the double-wedge phantom610. The user may employ the ultrasound images of the wedges 710 and720, like those illustrated in FIGS. 8A-8D, for feedback. If this isdone, the translation and rotation between the reference frame of thedouble-wedge phantom 610 and the pixel reference frame 235 will be moreprecise.

In step 375, the software computes the closed form formulation as isdone with exemplary system 200, except that the relative coordinatetransformation A (from the aforementioned AX=XB homogeneous equation)may correspond to the following relation:A=U _(k) W _(k,k+1) U _(k+1) ⁻¹where U_(k) is the transformation matrix from the coordinate frame ofthe double-wedge phantom 610 at pose k to the pixel coordinate frame245; U_(k+1) ⁻¹ is the inverse of the transformation matrix from thecoordinate frame of the double-wedge phantom 610 at pose k+1 to thepixel coordinate frame 245; and W_(k,k+1) is the transformation matrixfrom the coordinate frame of the double-wedge phantom 610 at pose k tothe double-wedge phantom 610 at pose k+1. Of these, W_(k,k+1) is known,since it depends on the precision to which the base plate 620 wasmachined and characterized. With the closed form formulation assembled,the software extracts a unique solution from the null space in step 380.

FIG. 9 illustrates an exemplary double-wedge phantom 910 according tothe present invention. The double-wedge phantom 910 has multiple sets ofwedges 710 and 720, each at different heights. Having multiple sets ofwedges 710 and 720 at different heights substantially enable thedivergence of the transmitted beam 705 to be characterized bydetermining the beam width BW at different heights, using the beam widthequation described above.

Exemplary system 600 may be used in a “bootstrap calibration” procedure,in which the probe calibration matrix ^(R)T_(P) is iteratively refined,and its accuracy and precision are improved. FIG. 10 illustrates anexemplary process 1000 for performing bootstrap calibration according tothe present invention.

Exemplary process 1000 includes process 300, in which ultrasound imagedata and probe position and angle data are collected. In this case, theultrasound images include an image of one of the double-wedge phantoms610 and the cross-wire structure 640. The bootstrapping calibrationtechnique works more effectively if the cross-wire structure 640 withinthe field of view of the ultrasound probe 210, but as far from thedouble-wedge phantom 610 as practicable. Within process 300, theultrasound probe 210 is placed such that it is sequentially centered andaligned relative to pose 1, pose 2, and pose 3. A probe calibrationmatrix ^(R)T_(P) is computed according to process 300. Process 300 isimplemented in such a way that a plurality of images may be acquired ateach pose, and the mean and standard deviation corresponding to theresulting probe calibration matrices are computed.

In step 1010, an inverse of the probe calibration matrix ^(R)T_(P) iscomputed, and the ultrasound image is reconstructed according to theinverse probe calibration matrix ^(R)T_(P). The reconstructed ultrasoundimage includes a reconstructed image of the cross-wire structure 640.

In step 1020, the reconstructed image of the cross-wire structure 640 iscompared with an actual image of the cross-wire structure, and astandard deviation is computed between the two images. The accuracy ofthe reconstructed image of the cross-wire structure (and thus theaccuracy of the probe calibration matrix ^(R)T_(P)) is assessedaccording to pre-determined accuracy requirements. If the probecalibration matrix ^(R)T_(P) is deemed sufficiently accurate, the probecalibration matrix ^(R)T_(P) is stored; if not, process 1000 proceeds tostep 1030.

In step 1030, the out-of-plane motion parameters are perturbed, andinput into process 300 as a new estimate for the U_(k), thetransformation matrix from the coordinate frame of the double-wedgephantom 610 at pose k to the pixel coordinate frame 245. The purpose ofperturbing the U_(k) matrix is to substantially encompass the range ofvalues for the elements of the U_(k) matrix such that the optimalversion of U_(k) will be selected.

In an additional embodiment of the present invention, the system 200illustrated in FIG. 2, in conjunction with exemplary process 300illustrated in FIG. 3, may be implemented without the use of a phantom260. In this exemplary embodiment, image registration may be done by useof speckle correlation. Speckle refers to a situation in which a targettissue contains a plurality of small acoustic scatterers that formpatterns of constructive and destructive interference within the tissue.The speckle pattern is generally stable, and may provide a pattern withsufficient spatial variability to substantially enable computingcorrelations between successive ultrasound images.

It will be apparent to those skilled in the art that variousmodifications and variation can be made in the present invention withoutdeparting from the spirit or scope of the invention. Thus, it isintended that the present invention cover the modifications andvariations of this invention provided they come within the scope of theappended claims and their equivalents.

1. A method for spatially calibrating an ultrasound probe, comprising:placing the ultrasound probe in a first position and orientationrelative to a phantom; measuring the first position and orientation ofthe ultrasound probe; acquiring a first ultrasound image of the phantom;determining a first spatial relationship between a phantom referenceframe and a pixel reference frame, based on the first ultrasound image;repositioning the ultrasound probe in a second position and orientationrelative to the phantom; measuring the second position and orientationof the ultrasound probe; acquiring a second ultrasound image of thephantom; determining a second spatial relationship between the phantomreference frame and the pixel reference frame, based on the secondultrasound image; and computing a probe calibration matrix based on thefirst position and orientation of the ultrasound probe, the firstspatial relationship, the second position and orientation of theultrasound probe, and the second spatial relationship.
 2. The method ofclaim 1, further comprising acquiring position and orientation data fromposition and angle encoder.
 3. The method of claim 1, whereindetermining the first spatial relationship includes: identifyingprominent phantom feature points in the first ultrasound image;identifying a center point of the phantom; and determining a coordinatetransformation between the center point of the phantom and a referenceframe corresponding to the ultrasound probe.
 4. The method of claim 3,wherein determining a coordinate transformation between the center pointof the phantom and a reference frame corresponding to the ultrasoundprobe includes: determining a translation between the center point ofthe phantom and a pixel location in the reference frame of theultrasound probe; and determining a rotation between the center point ofthe phantom and a pixel location in the reference frame of theultrasound probe.
 5. The method of claim 4, wherein determining arotation between the center point of the phantom and a pixel location inthe reference frame of the ultrasound probe includes representing therotation as a quaternion.
 6. The method of claim 1, wherein determininga first spatial relationship includes representing the first spatialrelationship as a quaternion.
 7. The method of claim 6, whereinextracting a unique solution includes using a unity constraint to afirst nine coefficients representing a rotation component to thecalibration matrix.
 8. The method of claim 1, wherein determining afirst spatial relationship includes representing the first spatialrelationship as a transformation matrix.
 9. The method of claim 1,wherein computing a probe calibration matrix includes: assembling thefirst position and orientation of the ultrasound probe, the firstspatial relationship, the second position and orientation of theultrasound probe, and the second spatial relationship into a closed formformulation; and extracting a unique solution from a null spacecorresponding to the closed form formulation.
 10. The method of claim 1,wherein computing a probe calibration matrix includes: assembling thefirst position and orientation of the ultrasound probe, the firstspatial relationship, the second position and orientation of theultrasound probe, and the second spatial relationship into a closed formformulation; extracting a rotational component from a null spacecorresponding to the closed form formulation; extracting a translationalcomponent from the null space corresponding to the closed formformulation; and extracting a vector of scale factors from the nullspace corresponding to the closed form formulation.
 11. The method ofclaim 1, wherein measuring the first position and orientation of theultrasound probe includes using optical markers that are disposed on theultrasound probe.
 12. The method of claim 1, wherein placing theultrasound probe in a first position relative to a phantom includesplacing the ultrasound probe in contact with a docking station, thedocking station having a position and orientation that is substantiallyfixed relative to the phantom.
 13. A system for performingintra-operative calibration of an ultrasound probe, comprising: aposition and angle encoder for measuring a position and angle of theultrasound probe; a phantom providing a reference element and a datasystem configured [having a computer readable medium encoded with aprogram] for computing a probe calibration matrix according to a closedform formulation, and according to a relative change between a firstlocation corresponding with the reference element in a first ultrasoundimage and a second location corresponding with the reference element ina second ultrasound image, wherein the first ultrasound imagecorresponds to a first ultrasound probe position, and the secondultrasound image corresponds to a second ultrasound probe position. 14.The system of claim 13, wherein the first location includes a prominentfeature point.
 15. The system of claim 13, wherein the first locationincludes a speckle pattern.
 16. The system of claim 13, wherein thephantom includes a wire arranged substantially in an N-shape.
 17. Thesystem of claim 13, wherein the phantom includes two substantiallyparallel plates.
 18. The system of claim 13, wherein the phantomincludes two wedges.
 19. The system of claim 13, further comprising adocking station, the docking station having a substantially fixedposition and orientation.
 20. The system of claim 13, wherein theposition and angle encoder includes optical markers that are disposed onthe ultrasound probe.